The problem is to solve the equation $3x^2 - 18 = 0$ using the square root property.

AlgebraQuadratic EquationsSolving EquationsSquare Root Property
2025/4/15

1. Problem Description

The problem is to solve the equation 3x218=03x^2 - 18 = 0 using the square root property.

2. Solution Steps

First, we want to isolate the x2x^2 term. Add 18 to both sides of the equation:
3x218+18=0+183x^2 - 18 + 18 = 0 + 18
3x2=183x^2 = 18
Next, divide both sides by 3:
3x23=183\frac{3x^2}{3} = \frac{18}{3}
x2=6x^2 = 6
Now, we can apply the square root property. Take the square root of both sides:
x2=±6\sqrt{x^2} = \pm\sqrt{6}
x=±6x = \pm\sqrt{6}
So the two solutions are x=6x = \sqrt{6} and x=6x = -\sqrt{6}.

3. Final Answer

6,6\sqrt{6}, -\sqrt{6}

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